The values of a physiological parameter and its time derivatives, detected at different times by different sensory receptors, are processed by the sensorimotor system to predict the time evolution of the parameter and convey appropriate control commands acting with minimum latency (few milliseconds) from the sensory stimulus. We have derived a power-series expansion (U-expansion) to simulate the fast prediction strategy of the sensorimotor system. Given a time-function , a time-instant , and a time-increment , the U-expansion enables the calculation of from and the values of the derivatives of at arbitrarily different times , instead of time as in the Taylor series. For increments significantly greater than the maximum among the differences , the error associated with truncation of the U-expansion at a given order closely equalizes the error of the corresponding Taylor series () truncated at the same order. Small values of and higher values of correspond to the high-frequency discharge of sensory neurons and the need for longer-term prediction, respectively. Taking inspiration from the sensorimotor system, the U-expansion can potentially provide an analytical background for the development of algorithms designed for the fast and accurate feedback control of nonlinear systems.
Keywords: feedback; nervous system; nonlinearity; prediction; sensory information; sensory receptor.